Next: The triple product Up: Applications of the Cross Previous: Applications of the Cross

Area vector of a parallelogram

The following picture shows two vectors as well as the parallelogram that is spanned by them.

The area of a parallelogram is simply the length times the height. In this case, the length of the parallelogram is tex2html_wrap_inline837 and the height is tex2html_wrap_inline839 . Thus, the area is tex2html_wrap_inline841 . Very often it is helpful to think of the area as a vector. The magnitude of the area vector is simply the ordinary area. Its direction is perpendicular to the surface itself. Thus, the area vector for the parallelogram above would point out of the screen.



Vector Calculus
Mon Jul 14 10:10:30 MST 1997